How to get solid render with wireframes and no shading
There are quite a few ways to accomplish this.


OpenGL

See this answer for details on setting up the wireframe.
Note that the Hidden Wire draw option can be useful for culling the wires on the back of the model without setting the color of the model to match the background.

See this answer for details on making the models in the viewport shadeless.

Pros: Very fast.  Usually no artifacts or missing lines. Works with optimal (curved) wireframes.

Cons: Total hack, requires setting theme colors to adjust the color of the wire and background. No control over line width.
Blender Internal

See these two answers for setting up the wireframe materials.

To make the base material shadeless, enable Shadeless in material settings > Shading:



To make it automatically match the background color, enable Mask Transparency in the base material and set the alpha to 0:





Pros: Works with optimal (curved) wireframes.

Cons: Can have issues with the Z offset causing missing lines or visible lines which should be occluded. Limited control over line styled/width.
Cycles

To get wireframes directly in cycles, see this question and the wireframe node.
To make a shadeless material in cycles, see this answer.

Pros: It's cycles

Cons: Perfect non-triangulated wireframes are not currently possible. There is a workaround with UV coordinates, however this results in line sizes relative to polygon size.
Wireframe modifier

The wireframe modifier generates actual mesh geometry representing the wireframe of the input mesh. Since the output is just a mesh, it works with both BI and Cycles.

See this answer for details on setting it up (answer is for cycles, but the process is identical for BI).

For shadeless renders, see the previous sections in this answer regarding BI and Cycles for descriptions of their respective methods of creating shadeless shaders.

Pros: Just works

Cons: Generates geometry; line thickness is defined in 3D space.
Freestyle

Freestyle is a line rendering engine which supports drawing over both BI and Cycles renders.

For cycles, see this answer.
For BI, see this answer.

Pros: Lots of control over line style etc.

Cons: Sometimes edges have gaps/other artifacts. Can be resource hungry.